6.RP.A.3 6th Grade Ratios & Proportional Relationships

Ratio Reasoning Application

Use ratio and rate reasoning to solve real-world and mathematical problems, using tables, tape diagrams, double number lines, and percents.

How to explain it

At this standard, students use equivalent ratio tables to find missing values and compare ratios, apply percent as a rate per 100 to find parts and wholes, and convert measurement units using ratio reasoning.

The anchor students hold onto: Multiply or divide BOTH quantities by the same scale factor to create equivalent ratios.

Ratio and rate reasoning (6.RP.A.3) bridges to proportional relationships (7.RP.A), scale problems, and percent applications in 7th grade.

Worked examples

Example 1 Ratio Table

Ratio table: 2 lemons : 3 cups.

Step 1Known ratio: 2 lemons : 3 cups

Step 24 lemons: x2 → 3 x 2 = 6 cups

Step 36 lemons: x3 → 3 x 3 = 9 cups

Step 48 lemons: x4 → 3 x 4 = 12 cups

Answer4 lemons → 6 cups · 6 lemons → 9 cups · 8 lemons → 12 cups

Example 2 Percent

Find 30% of 60.

Step 1Write percent as a fraction: 30/100

Step 2Multiply by the whole: 30/100 x 60

Step 3(30 x 60) / 100 = 1800 / 100 = 18

Step 430% of 60 = 18

Answer18

Common mistakes

What students write Scaled 2:3 by adding 4 to each term to get 6:7

The fix Multiply BOTH terms by 4: 2 x 4 = 8, 3 x 4 = 12. Adding changes the ratio relationship.

What students write To find 30% of 60, divide 60 ÷ 30 = 2

The fix Percent means per 100: write 30/100, then multiply by the whole: 30/100 x 60 = 18.

Teacher tip

Head off the two predictable errors before they happen. First: Multiply BOTH terms by 4: 2 x 4 = 8, 3 x 4 = 12. Adding changes the ratio relationship. Second: Percent means per 100: write 30/100, then multiply by the whole: 30/100 x 60 = 18.